Spectral methods for multimodal data analysis

Spectral methods have proven themselves as an important and versatile tool in a wide range of problems in the fields of computer graphics, machine learning, pattern recognition, and computer vision, where many important problems boil down to constructing a Laplacian operator and finding a few of its eigenvalues and eigenfunctions. Classical examples include the computation of diffusion distances on manifolds in computer graphics, Laplacian eigenmaps, and spectral clustering in machine learning. In many cases, one has to deal with multiple data spaces simultaneously. For example, clustering multimedia data in machine learning applications involves various modalities or ``views'' (e.g., text and images), and finding correspondence between shapes in computer graphics problems is an operation performed between two or more modalities. In this thesis, we develop a generalization of spectral methods to deal with multiple data spaces and apply them to problems from the domains of computer graphics, machine learning, and image processing. Our main construction is based on simultaneous diagonalization of Laplacian operators. We present an efficient numerical technique for computing joint approximate eigenvectors of two or more Laplacians in challenging noisy scenarios, which also appears to be the first general non-smooth manifold optimization method. Finally, we use the relation between joint approximate diagonalizability and approximate commutativity of operators to define a structural similarity measure for images. We use this measure to perform structure-preserving color manipulations of a given image

Atlas Construction for Measuring the Variability of Complex Anatomical Structures

RÉSUMÉ La recherche sur l'anatomie humaine, en particulier sur le cœur et le cerveau, est d'un intérêt particulier car leurs anomalies entraînent des pathologies qui sont parmi les principales causes de décès dans le monde et engendrent des coûts substantiels. Heureusement, les progrès en imagerie médicale permettent des diagnostics et des traitements autrefois impossibles. En contrepartie, la quantité phénoménale de données produites par ces technologies nécessite le développement d'outils efficaces pour leur traitement. L'objectif de cette thèse est de proposer un ensemble d'outils permettant de normaliser des mesures prélevées sur différents individus, essentiels à l'étude des caractéristiques de structures anatomiques complexes. La normalisation de mesures consiste à rassembler une collection d'images dans une référence commune, aussi appelée construction d'atlas numériques, afin de combiner des mesures provenant de différents patients. Le processus de construction inclut deux étapes principales; la segmentation d'images pour trouver des régions d'intérêts et le recalage d'images afin de déterminer les correspondances entres régions d'intérêts. Les méthodes actuelles de constructions d'atlas peuvent nécessiter des interventions manuelles, souvent fastidieuses, variables, et sont en outre limitées par leurs mécanismes internes. Principalement, le recalage d'images dépend d'une déformation incrémentales d'images sujettes a des minimums locaux. Le recalage n'est ainsi pas optimal lors de grandes déformations et ces limitations requièrent la nécessite de proposer de nouvelles approches pour la construction d'atlas. Les questions de recherche de cette thèse se concentrent donc sur l'automatisation des méthodes actuelles ainsi que sur la capture de déformations complexes de structures anatomiques, en particulier sur le cœur et le cerveau. La méthodologie adoptée a conduit à trois objectifs de recherche spécifiques. Le premier prévoit un nouveau cadre de construction automatise d'atlas afin de créer le premier atlas humain de l'architecture de fibres cardiaques. Le deuxième vise à explorer une nouvelle approche basée sur la correspondance spectrale, nommée FOCUSR, afin de capturer une grande variabilité de formes sur des maillages. Le troisième aboutit finalement à développer une approche fondamentalement différente pour le recalage d'images à fortes déformations, nommée les démons spectraux. Le premier objectif vise plus particulièrement à construire un atlas statistique de l'architecture des fibres cardiaques a partir de 10 cœurs ex vivo humains. Le système développé a mené à deux contributions techniques et une médicale, soit l'amélioration de la segmentation de structures cardiaques et l'automatisation du calcul de forme moyenne, ainsi que notamment la première étude chez l'homme de la variabilité de l'architecture des fibres cardiaques. Pour résumer les principales conclusions, les fibres du cœur humain moyen varient de +- 12 degrés, l'angle d'helix s'étend entre -41 degrés (+- 26 degrés) sur l'épicarde à +66 degrés (+- 15 degrés) sur l'endocarde, tandis que l'angle transverse varie entre +9 degrés (+- 12 degrés) et +34 degrés (+- 29 degrés) à travers le myocarde. Ces résultats sont importants car ces fibres jouent un rôle clef dans diverses fonctions mécaniques et électrophysiologiques du cœur. Le deuxième objectif cherche à capturer une grande variabilité de formes entre structures anatomiques complexes, plus particulièrement entre cortex cérébraux à cause de l'extrême variabilité de ces surfaces et de leur intérêt pour l'étude de fonctions cognitives. La nouvelle méthode de correspondance surfacique, nommée FOCUSR, exploite des représentations spectrales car l'appariement devient plus facile et rapide dans le domaine spectral plutôt que dans l'espace Euclidien classique. Dans sa forme la plus simple, FOCUSR améliore les méthodes spectrales actuelles par un recalage non rigide des représentations spectrales, toutefois, son plein potentiel est atteint en exploitant des données supplémentaires lors de la mise en correspondance. Par exemple, les résultats ont montré que la profondeur des sillons et de la courbure du cortex cérébral améliore significativement la correspondance de surfaces de cerveaux. Enfin, le troisième objectif vise à améliorer le recalage d'images d'organes ayant des fortes variabilités entre individus ou subis de fortes déformations, telles que celles créées par le mouvement cardiaque. La méthodologie amenée par la correspondance spectrale permet d'améliorer les approches conventionnelles de recalage d'images. En effet, les représentations spectrales, capturant des similitudes géométriques globales entre différentes formes, permettent de surmonter les limitations actuelles des méthodes de recalage qui restent guidées par des forces locales. Le nouvel algorithme, nommé démons spectraux, peut ainsi supporter de très grandes déformations locales et complexes entre images, et peut être tout autant adapté a d'autres approches, telle que dans un cadre de recalage conjoint d'images. Il en résulte un cadre complet de construction d'atlas, nommé démons spectraux multijoints, où la forme moyenne est calculée directement lors du processus de recalage plutôt qu'avec une approche séquentielle de recalage et de moyennage. La réalisation de ces trois objectifs spécifiques a permis des avancées dans l'état de l'art au niveau des méthodes de correspondance spectrales et de construction d'atlas, en permettant l'utilisation d'organes présentant une forte variabilité de formes. Dans l'ensemble, les différentes stratégies fournissent de nouvelles contributions sur la façon de trouver et d'exploiter des descripteurs globaux d'images et de surfaces. D'un point de vue global, le développement des objectifs spécifiques établit un lien entre : a) la première série d'outils, mettant en évidence les défis à recaler des images à fortes déformations, b) la deuxième série d'outils, servant à capturer de fortes déformations entre surfaces mais qui ne reste pas directement applicable a des images, et c) la troisième série d'outils, faisant un retour sur le traitement d'images en permettant la construction d'atlas a partir d'images ayant subies de fortes déformations. Il y a cependant plusieurs limitations générales qui méritent d'être investiguées, par exemple, les données partielles (tronquées ou occluses) ne sont pas actuellement prises en charge les nouveaux outils, ou encore, les stratégies algorithmiques utilisées laissent toujours place à l'amélioration. Cette thèse donne de nouvelles perspectives dans les domaines de l'imagerie cardiaque et de la neuroimagerie, toutefois, les nouveaux outils développés sont assez génériques pour être appliqués a tout recalage d'images ou de surfaces. Les recommandations portent sur des recherches supplémentaires qui établissent des liens avec la segmentation à base de graphes, pouvant conduire à un cadre complet de construction d'atlas où la segmentation, le recalage, et le moyennage de formes seraient tous interdépendants. Il est également recommandé de poursuivre la recherche sur la construction de meilleurs modèles électromécaniques cardiaques à partir des résultats de cette thèse. En somme, les nouveaux outils offrent de nouvelles bases de recherche et développement pour la normalisation de formes, ce qui peut potentiellement avoir un impact sur le diagnostic, ainsi que la planification et la pratique d'interventions médicales.----------ABSTRACT Research on human anatomy, in particular on the heart and the brain, is a primary concern for society since their related diseases are among top killers across the globe and have exploding associated costs. Fortunately, recent advances in medical imaging offer new possibilities for diagnostics and treatments. On the other hand, the growth in data produced by these relatively new technologies necessitates the development of efficient tools for processing data. The focus of this thesis is to provide a set of tools for normalizing measurements across individuals in order to study complex anatomical characteristics. The normalization of measurements consists of bringing a collection of images into a common reference, also known as atlas construction, in order to combine measurements made on different individuals. The process of constructing an atlas involves the topics of segmentation, which finds regions of interest in the data (e.g., an organ, a structure), and registration, which finds correspondences between regions of interest. Current frameworks may require tedious and hardly reproducible user interactions, and are additionally limited by their computational schemes, which rely on slow iterative deformations of images, prone to local minima. Image registration is, therefore, not optimal with large deformations. Such limitations indicate the need to research new approaches for atlas construction. The research questions are consequently addressing the problems of automating current frameworks and capturing global and complex deformations between anatomical structures, in particular between human hearts and brains. More precisely, the methodology adopted in the thesis led to three specific research objectives. Briefly, the first step aims at developing a new automated framework for atlas construction in order to build the first human atlas of the cardiac fiber architecture. The second step intends to explore a new approach based on spectral correspondence, named FOCUSR, in order to precisely capture large shape variability. The third step leads, finally, to a fundamentally new approach for image registration with large deformations, named the Spectral Demons algorithm. The first objective aims more specifically at constructing a statistical atlas of the cardiac fiber architecture from a unique human dataset of 10 ex vivo hearts. The developed framework made two technical, and one medical, contributions, that are the improvement of the segmentation of cardiac structures, the automation of the shape averaging process, and more importantly, the first human study on the variability of the cardiac fiber architecture. To summarize the main finding, the fiber orientations in human hearts has been found to vary with about +- 12 degrees, the range of the helix angle spans from -41 degrees (+- 26 degrees) on the epicardium to +66 degrees (+- 15 degrees) on the endocardium, while, the range of the transverse angle spans from +9 degrees (+- 12 degrees) to +34 degrees (+- 29 degrees) across the myocardial wall. These findings are significant in cardiology since the fiber architecture plays a key role in cardiac mechanical functions and in electrophysiology. The second objective intends to capture large shape variability between complex anatomical structures, in particular between cerebral cortices due to their highly convoluted surfaces and their high anatomical and functional variability across individuals. The new method for surface correspondence, named FOCUSR, exploits spectral representations since matching is easier in the spectral domain rather than in the conventional Euclidean space. In its simplest form, FOCUSR improves current spectral approaches by refining spectral representations with a nonrigid alignment; however, its full power is demonstrated when using additional features during matching. For instance, the results showed that sulcal depth and cortical curvature improve significantly the accuracy of cortical surface matching. Finally, the third objective is to improve image registration for organs with a high inter-subject variability or undergoing very large deformations, such as the heart. The new approach brought by the spectral matching technique allows the improvement of conventional image registration methods. Indeed, spectral representations, which capture global geometric similarities and large deformations between different shapes, may be used to overcome a major limitation of current registration methods, which are in fact guided by local forces and restrained to small deformations. The new algorithm, named Spectral Demons, can capture very large and complex deformations between images, and can additionally be adapted to other approaches, such as in a groupwise configuration. This results in a complete framework for atlas construction, named Groupwise Spectral Demons, where the average shape is computed during the registration process rather than in sequential steps. The achievements of these three specific objectives permitted advances in the state-of-the-art of spectral matching methods and of atlas construction, enabling the registration of organs with significant shape variability. Overall, the investigation of these different strategies provides new contributions on how to find and exploit global descriptions of images and surfaces. From a global perspective, these objectives establish a link between: a) the first set of tools, that highlights the challenges in registering images with very large deformations, b) the second set of tools, that captures very large deformations between surfaces but are not applicable to images, and c) the third set of tools, that comes back on processing images and allows a natural construction of atlases from images with very large deformations. There are, however, several general remaining limitations, for instance, partial data (truncated or occluded) is currently not supported by the new tools, or also, the strategy for computing and using spectral representations still leaves room for improvement. This thesis gives new perspectives in cardiac and neuroimaging, yet at the same time, the new tools remain general enough for virtually any application that uses surface or image registration. It is recommended to research additional links with graph-based segmentation methods, which may lead to a complete framework for atlas construction where segmentation, registration and shape averaging are all interlinked. It is also recommended to pursue research on building better cardiac electromechanical models from the findings of this thesis. Nevertheless, the new tools provide new grounds for research and application of shape normalization, which may potentially impact diagnostic, as well as planning and performance of medical interventions

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Digital Restoration of Damaged Historical Parchment

In this thesis we describe the development of a pipeline for digitally restoring damaged historical parchment. The work was carried out in collaboration with London Metropolitan Archives (LMA), who are in possession of an extremely valuable 17th century document called The Great Parchment Book. This book served as the focus of our project and throughout this thesis we demonstrate our methods on its folios. Our aim was to expose the content of the book in a legible form so that it can be properly catalogued and studied. Our approach begins by acquiring an accurate digitisation of the pages. We have developed our own 3D reconstruction pipeline detailed in Chapter 5 in which each parchment is imaged using a hand-held digital-SLR camera, and the resulting image set is used to generate a high-resolution textured 3D reconstruction of each parchment. Investigation into methods for flatting the parchments demonstrated an analogy with surface parametrization. Flattening the entire parchment globally with various existing parametrization algorithms is problematic, as discussed in Chapters 4, 6, and 7, since this approach is blind to the distortion undergone by the parchment. We propose two complementary approaches to deal with this issue. Firstly, exploiting the fact that a reader will only ever inspect a small area of the folio at a given time, we proposed a method for performing local undistortion of the parchments inside an interactive viewer application. The application, described in Chapter 6, allows a user to browse a parchment folio as the application un-distorts in real-time the area of the parchment currently under inspection. It also allows the user to refer back to the original image set of the parchment to help with resolving ambiguities in the reconstruction and to deal with issues of provenance. Secondly, we proposed a method for estimating the actual deformation undergone by each parchment when it was damaged by using cues in the text. Since the text was originally written in straight lines and in a roughly uniform script size, we can detect the the variation in text orientation and size and use this information to estimate the deformation. in Chapter 7 we then show how this deformation can be inverted by posing the problem as a Poisson mesh deformation, and solving it in a way that guarantees local injectivity, to generate a globally flattened and undistorted image of each folio. We also show how these images can optionally be colour corrected to remove the shading cues baked into the reconstruction texture, and the discolourations in the parchment itself, to further improve legibility and give a more complete impression that the parchment has been restored. The methods we have developed have been very well received by London Metropolitan Archives, as well the the larger archival community. We have used the methods to digitise the entire Great Parchment Book, and have demonstrated our global flattening method on eight folios. As of the time of writing of this thesis, our methods are being used to virtually restore all of the remaining folios of the Great Parchment Book. Staff at LMA are also investigating potential future directions by experimenting with other interesting documents in their collections, and are exploring the possibility of setting up a service which would give access to our methods to other archival institutions with similarly damaged documents

Multimedia Forensics

This book is open access. Media forensics has never been more relevant to societal life. Not only media content represents an ever-increasing share of the data traveling on the net and the preferred communications means for most users, it has also become integral part of most innovative applications in the digital information ecosystem that serves various sectors of society, from the entertainment, to journalism, to politics. Undoubtedly, the advances in deep learning and computational imaging contributed significantly to this outcome. The underlying technologies that drive this trend, however, also pose a profound challenge in establishing trust in what we see, hear, and read, and make media content the preferred target of malicious attacks. In this new threat landscape powered by innovative imaging technologies and sophisticated tools, based on autoencoders and generative adversarial networks, this book fills an important gap. It presents a comprehensive review of state-of-the-art forensics capabilities that relate to media attribution, integrity and authenticity verification, and counter forensics. Its content is developed to provide practitioners, researchers, photo and video enthusiasts, and students a holistic view of the field

Signal Processing in Wireless Communications: Device Fingerprinting and Wide-Band Interference Rejection

The rapid progress of wireless communication technologies that has taken place in recent years has significantly improved the quality of everyday life. However with this expansion of wireless communication systems come significant security threats and significant technological challenges, both of which are due to the fact that the communication medium is shared. The ubiquity of open wireless Internet access networks creates a new avenue for cyber-criminals to impersonate and act in an unauthorized way. The increasing number of deployed wide-band wireless communication systems entails technological challenges for effective utilization of the shared medium, which implies the need for advanced interference rejection methods. Wireless security and interference rejection in wide-band wireless communications are therefore often considered as the two main challenges in wireless network\u27s design and research. Important aspects of these challenges are illuminated and addressed in this dissertation. This dissertation considers signal processing approaches for exploiting or mitigating the effects of non-ideal components in wireless communication systems. In the first part of the dissertation, we introduce and study a novel, model-based approach to wireless device identification that exploits imperfections in the transmitter caused by manufacturing process nonidealities. Previous approaches to device identification based on hardware imperfections vary from transient analysis to machine learning but have not provided verifiable accuracy. Here, we detail a model-based approach, that uses statistical models of RF transmitter components: digital-to-analog converter, power amplifier and RF oscillator, which are amenable for analysis. Our proposed approach examines the key device characteristics that cause anonymity loss, countermeasures that can be applied by the nodes to regain the anonymity, and ways of thwarting such countermeasures. We develop identification algorithms based on statistical signal processing methods and address the challenging scenario when the units that need to be distinguished from one another are of the same model and from the same manufacturer. Using simulations and measurements of components that are commonly used in commercial communications systems, we show that our anonymity breaking techniques are effective. In the second part of the dissertation, we consider innovative approaches for the acquisition of frequency-sparse signals with wide-band receivers when a weak signal of interest is received in the presence of a very strong interference, and the effects of the nonlinearities in the low-noise amplifier at the receiver must be mitigated. All samples with amplitude above a given threshold, dictated by the linear input range of the receiver, are discarded to avoid the distortion caused by saturation of the low noise amplifier. Such a sampling scheme, while avoiding nonlinear distortion that cannot be corrected in the digital domain, poses challenges for signal reconstruction techniques, as the samples are taken non-uniformly, but also non-randomly. The considered approaches fall into the field of compressive sensing (CS); however, what differentiates them from conventional CS is that a structure is forced upon the measurement scheme. Such a structure causes a violation of the core CS assumption of the measurements\u27 randomness. We consider two different types of structured acquisition: signal independent and signal dependent structured acquisition. For the first case, we derive bounds on the number of samples needed for successful CS recovery when samples are drawn at random in predefined groups. For the second case, we consider enhancements of CS recovery methods when only small-amplitude samples of the signal that needs to be recovered are available for the recovery. Finally, we address a problem of spectral leakage due to the limited processing block size of block processing, wide-band receivers and propose an adaptive block size adjustment method, which leads to significant dynamic range improvements

Multimedia Forensics

This book is open access. Media forensics has never been more relevant to societal life. Not only media content represents an ever-increasing share of the data traveling on the net and the preferred communications means for most users, it has also become integral part of most innovative applications in the digital information ecosystem that serves various sectors of society, from the entertainment, to journalism, to politics. Undoubtedly, the advances in deep learning and computational imaging contributed significantly to this outcome. The underlying technologies that drive this trend, however, also pose a profound challenge in establishing trust in what we see, hear, and read, and make media content the preferred target of malicious attacks. In this new threat landscape powered by innovative imaging technologies and sophisticated tools, based on autoencoders and generative adversarial networks, this book fills an important gap. It presents a comprehensive review of state-of-the-art forensics capabilities that relate to media attribution, integrity and authenticity verification, and counter forensics. Its content is developed to provide practitioners, researchers, photo and video enthusiasts, and students a holistic view of the field

Autocalibrating vision guided navigation of unmanned air vehicles via tactical monocular cameras in GPS denied environments

This thesis presents a novel robotic navigation strategy by using a conventional tactical monocular camera, proving the feasibility of using a monocular camera as the sole proximity sensing, object avoidance, mapping, and path-planning mechanism to fly and navigate small to medium scale unmanned rotary-wing aircraft in an autonomous manner. The range measurement strategy is scalable, self-calibrating, indoor-outdoor capable, and has been biologically inspired by the key adaptive mechanisms for depth perception and pattern recognition found in humans and intelligent animals (particularly bats), designed to assume operations in previously unknown, GPS-denied environments. It proposes novel electronics, aircraft, aircraft systems, systems, and procedures and algorithms that come together to form airborne systems which measure absolute ranges from a monocular camera via passive photometry, mimicking that of a human-pilot like judgement. The research is intended to bridge the gap between practical GPS coverage and precision localization and mapping problem in a small aircraft. In the context of this study, several robotic platforms, airborne and ground alike, have been developed, some of which have been integrated in real-life field trials, for experimental validation. Albeit the emphasis on miniature robotic aircraft this research has been tested and found compatible with tactical vests and helmets, and it can be used to augment the reliability of many other types of proximity sensors